Machine Learning Based Antenna Array Beamforming: Dokuz Eylül University Graduate School of Natural and Applied Sciences
Machine Learning Based Antenna Array Beamforming: Dokuz Eylül University Graduate School of Natural and Applied Sciences
Machine Learning Based Antenna Array Beamforming: Dokuz Eylül University Graduate School of Natural and Applied Sciences
by
Muhammed UĞUR KILIÇ
January, 2023
İZMİR
MACHINE LEARNING BASED ANTENNA ARRAY
BEAMFORMING
by
Muhammed UĞUR KILIÇ
January, 2023
İZMİR
M.Sc THESIS EXAMINATION RESULT FORM
.............................................................................
Asst. Prof. Dr. Özgür Tamer
Supervisor
........................................................................ ........................................................................
Doç. Dr. Hatice Doğan Prof. Dr. Mustafa Seçmen
ii
ACKNOWLEDGEMENTS
My sincere thanks,
To my family who made me come to this day and always supported me,
To my dear friends Mazlum Unay and Ulaş Yüksel who helped me in this work,
To my wife Burcu Mutlu Kılıç, who supported me in every difficulty and stood by
me in all my moments.
iii
MACHINE LEARNING BASED ANTENNA ARRAY BEAMFORMING
ABSTRACT
The present study focuses on estimating proper weights for beamforming of an array
beamforming with the help of a neural network structure. Training set was created from
different users located at different angles. Neural network classifies signal strength
calculated for each user. Test user locations are selected randomly and according to
these locations test steering vectors are created.Algorithm starts and creates classified
signal strength and arrival angle outputs according to test steering vectors. It is aimed
to provide better quality mobile network service for users in the concentrated region in
cases that progress compared to the trained network.
iv
MAKİNE ÖĞRENMESİ TEMELLİ ANTEN DİZİSİ HÜZME
YÖNLENDİRME
ÖZ
Bu çalışma, bir sinir ağı yapısı yardımıyla bir dizi hüzme şekillendirmenin hüzme
şekillendirme için uygun ağırlıkları tahmin etmeye odaklanmaktadır. Farklı açılarda
konumlanmış farklı kullanıcılardan eğitim seti oluşturulmuştur. Sinir ağı, her
kullanıcı için hesaplanan sinyal gücünü ve açısını sınıflandırır. Test kullanıcı
lokasyonları rastgele seçilir ve bu lokasyonlara göre test yönlendirme vektörleri
oluşturulur. Algoritma test yönlendirme vektörlerine göre sınıflandırılmış sinyal gücü
ve varış açısı çıktıları oluşturur.Eğitimli ağa göre ilerleme gösteren durumlarda,
yoğunlaşan bölgedeki kullanıcılara daha kaliteli mobil ağ hizmeti sunulması
amaçlanmaktadır.
Anahtar kelimeler: Hüzlemeleme, sinir ağı, sinir ağı ile haberleşme, hüzmeleme ile
mobil haberleşme, sinir ağı ile hüzmeleme, makine öğrenmesi.
v
CONTENTS
Page
vi
2.7.1 Multi Layer Neural Network ......................................................... 26
2.7.1.1 Training Step ....................................................................... 26
2.7.2 Flowchart of The Training Algorithm ............................................. 27
REFERENCES.......................................................................................... 45
vii
LIST OF FIGURES
Page
Figure 2.6 Parasitic Antenna Array and Radiation (Electronics Desk, 2012) .......8
viii
Figure 3.2 Beam Pattern and Azimuth Plot without Beamforming .................. 29
Figure 3.5 Beam Pattern and Azimuth Plot for First Beamforming .................. 31
Figure 3.6 Beam Pattern and Azimuth Plot for 9th Beamforming.................... 32
ix
LIST OF TABLES
Page
x
CHAPTER ONE
INTRODUCTION
Beamforming is used to change the direction of signal for maximum efficiency and
quality signal and decrease interference in communication system. In 1905, the
German physicist and inventor Karl F. Braun presented the first public demonstration
of beamforming. Braun built a phased array by placing three antennas so that
radiation was amplified in one direction and reduced in another. (Braun, 1909).
1
When Warren McCulloch and Walter Pitts developed a computational model for
neural networks based on threshold logic algorithms in 1943, the history of artificial
neural networks (ANN) officially began. This method provided the path for the
division of the research into two methods. One method emphasized biological
processes, while the other concentrated on using neural networks to create artificial
intelligence (Warren & Pitts, 1943).
The Hebbian learning theory was developed by D. O. Hebb in the late 1940s and is
based on the brain plasticity mechanism. Unsupervised learning is hebbian learning.
Feed-forward neural networks and recurrent neural networks evolved between 2009
and 2012 in Eight worldwide contests in pattern recognition and machine learning were
won by Schmidhuber’s research team.
When it comes to today, the importance of machine learning has increased with
the developments in the field of communication and it has started to take its place in
the field of telecommunication. Some of the articles used in this field and applied in
different telecommunication fields are as follows;
In July 25, 2016, neural network is performed with using beamforming technique
called mimimum variance distortionless response (MVDR). The trained NN can serve
as an adaptive beamformer that enables a linear antenna array to orient the main lobe
to a desired signal and inserts nulls into the corresponding interference signals in the
2
presence of additional zero-average Gaussian noise (Zaharis, 2016).
In Dec, 2021, It is aimed to determine the precoder with the neural network by using
the user’s location.It allows to reduce or even eliminate the need for pilot symbols,
depending on how the location is obtained(Le Magoarou & Crussière, 2021).
3
Article published in International Journal of Computer Applications in Nov,2015
by Adheed H. Sallomi,Sulaiman Ahmed, as we used in this thesis , this study focuses
on the study that calculates the optimum weights on the adaptive beam using the
elman neural network. In this study, Levenberg Marquardt (LM) algorithm and
Resilient Backpropagation (Rprop) algorithms are used comparatively (Sallom &
Ahmed, 2015).
In article written by Murat Güreken, the real-time target tracking issue is solved
with a Neural Network (NN) based beamforming technique. The approach is used to
two different types of arrays: circular and linear.SNR (Signal to Noise Ratio) value
was calculated by calculating the direction of arrival angle (DOA) according to the
GPS-based location of the users. Then, the error was calculated by running NN training
according to the angle and SNR (Güreken, 2009).
In this project, it is aimed to form the signal to improve the user oriented signal
level and quality by creating data for the learning mechanism by using receivers at
different points. In the first case, the function defined to provide the best between the
users whose location is known and the base station is used and the steering vectors are
calculated. Afterwards, by training with this data with neural network structure, the
system will aim to increase the user experience by shaping the signal according to the
location information received from the system user, without using the function.
4
CHAPTER TWO
THEORETICAL BACKGROUND
A metallic object called an antenna is used to receive and/or transmit radio waves.
Numerous distinct antenna types with unique characteristics are employed in radio
systems for various applications. Antennas can be categorized in a number of ways.
The following list of common antenna types;
5
Figure 2.2 Rubber ducky antenna on 446 MHz UHF(Wikipedia, 2012b)
The dipole antenna’s two poles or two conducting components are indicated by the
name "di-pole." As can be seen, the fundamental antenna includes a two-conductor
element. The dipole antenna is typically split in the middle, and these are typically on
the same axis. (Basu, 2010).
6
2.2 Array Antenna Systems
Array antennas are made up of numerous antennas that operate as one compound
antenna when combined.
N
In × e j×(n−1)×(cosφ) AF = 1 + I1 e j×(kd cos θ+β1 ) + I2 e j×(2kd cos θ+β2 + ...
X
AF = (2.1)
n=1
φ = kdcosθ + β (2.2)
e j × N × (φ) − 1
AF = (2.5)
e j × (φ) − 1
N ×φ
(sin )
AF = (e( j×(N−1)×φ)/2 ) × ( 2 ) (S eanV.Hum, 2021). (2.6)
φ
(sin )
2
7
Types of Arrays:
Parasitic: Some elements not connected to source. They re-radiate power from other
elements.
Phased: All elements connected to source. This type is used for in this thesis.
Figure 2.6 Parasitic Antenna Array and Radiation (Electronics Desk, 2012)
8
For broadside antenna main lobe at at =0 or at=180
φ = kdcosθ + β = 0 (2.7)
N ×φ
1 (sin 2 )
AF = × φ (2.8)
N (sin )
2
φ = kd × (cos θ ± 1) (2.9)
N ×φ
1 (sin 2 )
AF = × φ (2.10)
N (sin )
2
9
2.2.1 Phased Array Antenna Systems
Multiple emitters/receivers are found in phased array antennas, which are utilized
for beamforming in RF applications, particularly high frequency ones. There are three
common uses for WiFi, chirped radar, and 5G. (Cadence, 2021). By altering the phase
difference between the signal transmitted to each transmitter in the array, a phased
array antenna enables beamforming. This eliminates the need for the antenna to be
physically moved in order to regulate and steer the radiation pattern to a target
(Torres-Rosario, 2005).
10
Figure 2.8 A Phased Array System (Tougaw, 2018)
The array factor takes into account array characteristics like the separation between
elements and the progressive phase difference between each element.
N
X
AF = e j×(n−1)×(kdcosθ+β) (2.11)
n=1
where, N are the number of elements, is the ongoing phase shift between each antenna
element, d is the distance between each element in the array, A is the input signal or
element factor and s is steering vector.
e j×θ0
j×θ1
e
s(t) = [s0(t), s1(t).......sm(t)] = .
(2.12)
..
j×θ.m
e
11
2.2.1.1 Uniform Line Array
A group of sensor components that are uniformly spaced along a line constitute a
uniform linear array. A dipole antenna that can send and receive electromagnetic waves
is the most popular kind of sensor. It is thought that plane waves of electromagnetic
waves are how they reach the array. This indicates that the transmitter and receiver are
separated by a significant distance. The spacing ’d’ between array elements must be
less than or equal to half the wavelength (Ahmed, 2018).
12
2.2.1.2 Uniform Planar Array
13
2.3 Smart Antenna System
The two main groups of smart antennas differ in the following ways in terms of
transmitting strategy options;
Figure 2.11 Switched and Adaptive Array System (K. A. Gotsis & Sahalos, 2019)
14
2.4 Beamforming
When creating an array, numerous factors must be taken into account. In array
designs, variables including array geometry, element spacing, element lattice structure,
and element tapering are frequently used. Before the final design is executed, it is also
critical to define the impacts of mutual coupling. After the array architecture has been
configured initially, architectural partitioning may be repeatedly assessed against the
system performance objectives. In systems using millimeter waves, the array’s surface
area decreases according to wavelength size. An antenna array created for millimeter
wave frequencies, for instance, can be up to 100 times smaller than one created for
microwave frequencies. You can attain a high beamforming gain by constructing an
array with more antenna components. As beams are directed in a certain direction, the
highly directional beam helps to mitigate the increasing path loss at higher frequencies
of operation (Mathworks, 2020).
15
There are three types of beamforming seperated each other by physical elements
and connections;
Analog beamforming sends same signal to each antenna element and controlling the
phase of each transmitted signal.
Digital beamforming uses various signals for each antenna. It needs the carrier
frequency of the processed signal to be upconverted after a crossover RF chain that
comprises digital-to-analog (D/A) converters, mixers, and power amplifiers since it
regulates the phase and amplitude of the signal (Ali & Nordin, 2017).
Hybrid beamforming mixes digital and analog beamforming, which means that part
of the beamforming is done digitally in the baseband and portion is done by analog RF
beamformers (Kim, 2013).
16
2.5 Machine Learning
Understanding data structure and fitting it into models that people can use and
comprehend is the goal of machine learning. The majority of jobs in machine learning
may be divided into broad groups. These categories define how learning occurs, and
supervised learning and unsupervised learning are two of the most popular machine
learning techniques (Pedamkar, 2022).
17
2.6 Neural Network
18
There are three important types of neural network are used to improve performance
of models;
Counting the number of inputs, outputs, hidden neurons, and hidden layers is part
of defining an FNN design (Facundo Bre & Fachinott, 2018).A simple FNN is shown
below;
19
2.6.2 Convolution Neural Networks
One of the most popular deep neural networks is Convolutional Neural Network.
Its name is derived from the linear convolution process between matrices in
mathematics. The reduction of ANN’s parameter count is CNNs’ most advantageous
feature. Convolutional, non-linear, pooling, and fully-connected layers are among the
many layers that make up CNN. Image, video, and speech recognition are all made
possible by CNN (S. Albawi & Al-Zawi, 2017).
20
2.6.3 Recurrent Neural Network
Neural network types have some differences. Some of the main ones are listed in
the table below.
21
Many training algorithms have been proposed for RNN also called feedback neural;
Elman Neural Network, the first type of neural network employed in this study, is
made up of several models of neuronal cells that are organized in accordance with
predetermined criteria. Elman’s 1990 research on the backpropagation (BP) neural
network led to the development of a straightforward RNN known as the Elman neural
network. (D. E. Rumelhart & Williams, 1986). Comparing to traditional neural
networks, ENN has additional inputs from the hidden layer, which forms a new
layer-the context layer (Guanghua Ren & Zeng, 2018).
Jordan networks and Elman networks are related. Instead of the hidden nodes, the
context units are provided from the output layer. Context units in the Jordan network
are also called state layers. They have a recurring bond with themselves (Cruse, 2006).
22
Figure 2.19 Jordan Network (Caceres, 2020).
Recurrent neural networks are recursive artificial neural networks with a certain
structure that of a linear chain.
23
The Hopfield network is an RNN in which all the links between the layers have
equal dimensions. It requires static inputs and is therefore not a generic RNN because
it does not handle pattern sequence(Hopfield, 1982).
24
2.7 Mathematical Model Of The Project
The array factor takes into account array factors such as the phase difference
between each element and the distance between elements.
XN
AF = e j×(n−1)×(kdcosθ+β) (2.14)
n=1
where N denotes the number of antenna elements, is the progressive phase shift
between each antenna element, d denotes the inter-element distance between each
element in the array, A denotes the input signal or element factor, and s denotes the
steering vector.
e j×θ0
j×θ1
e
s(t) = [s0(t), s1(t).......sm(t)] = .
(2.15)
..
j×θ.m
e
Q is called the angle vector or arrival angle vector from receiver sites.Arrival angles
coming from all receiver sites are changes and steering vector weights ( phase angles)
are updated. In this way, the output signal is formed to the locations of the users. n(t)
is additional noise. Signal strength, returned as in dBm for each receiver sites.
S S = 10log10(P/1MW) (2.16)
P is the power of the signal on the receiver side coming from transmitter.
25
2.7.1 Multi Layer Neural Network
Network has more than one neurons,each neurons connected to next layer multiple
neuron.
• Firstly, random users angle and signal strength or quality is taken an stored in
angle and signal strength vector.
• The weights are phase angle=0 and steering vector is equal to 1 for all elements.
e j = |Y j − Z| (2.17)
W j = W j − 1 + r × e j × Y j × f −1 X (2.18)
(r=learning rate)
Wk + 1 = Wk − |J × J T + u × I|−1 J T × e (2.19)
(J is the Jacobian matrix that contains first derivatives of the network errors with
respect to the weights and biases, and e is a vector of network errors)
26
2.7.2 Flowchart of The Training Algorithm
27
CHAPTER THREE
APPLICATIONS AND RESULTS
In this section , the method for beamforming and neural network systems having
different algorithm , results from the different user locating different place will be
shown. For each beamform creating for each user are shown step by step, finally
training and test datas will be evaluated.
Firstly, we begin by creating transmitter or base station site with Matlab.We define
transmitter location, frequency and antenna type shown below in table;
Then, the angle of arrival according to the locations of the receivers and the steering
vector with this angle are calculated. Each receiver creates its own steering vector or
array factor. This data is then defined in an MxN sized matrix to be used for the neural
network algorithm. Each column has steering vector values specified for individual
users.
28
Firstly, defining transmitter site to represent a base station operating 2.1 Ghz with
40 watt of power. Location of base station is chosen as Buca/Izmir.
Then, after determining the antenna type and array type of the base station, the beam
pattern before beamforming (it varies according to the antenna type) is as follows;
29
Then, 1000 different locations are determined to be used in training by the recipient.
The angle and signal levels between the transmitter and receiver were calculated using
a separate link for each user. The link established between the first user and the base
station is as follows;
Thanks to the steering vectors created for each user the output signal is formed
and basic beamforming is applied. A different phase angle value is applied to each
antenna element according to the arrival angle value and the beam is formed. The
basic beamforming structure applied in this project is as follows;
30
Figure 3.4 Beamforming Block Diagram()
After taking first angle of user between base station and creating new form of
signal using beamforming technique mentioned above for first user to achieve
maximum signal strength as follows;
Figure 3.5 Beam Pattern and Azimuth Plot for First Beamforming
31
Figure 3.6 Beam Pattern and Azimuth Plot for 9th Beamforming
Data set taken before from each user for neural network training is used.Neural
network uses signal strength or signal quality and arrival angle received with base
station to predict the best beamforming vector at the each receiver site. With the test
steering vector data, best signal strength are calculated for each user.
The results obtained using different algorithms including different types of neural
networks, which were mentioned earlier in section 2, will be observed and the results
related to the beamforming architecture will be examined.
32
3.3 Results
Firstly, the test angle values were studied with Elman network by using the angle
values between the receiver and the base station. Relevant values were classified with
30 degrees difference between -180 and 180 degree angle values and approximate
results were estimated by Elman network algorithm. Afterwards, the learning rate
values were changed from the training options and the value that would give the
optimum result was found. The best value for the Elman network was chosen as 0.5.
The training values determined for Elman network are as follow;
33
Figure 3.8 Elman Neural Network Training
After training , estimation values are assigned 1xN vector. N is equal to 1000 which
is test user number. For first and 17th user, estimations are true and it is shown below;
Table 3.3 Original & Estimation Arrival Angle Value for 1st & 17th Users
Training Training
Original Original
Output Output
Value Value
First User 17th User
angtest(1,1)= angtest(:,17)=
-0.1920 -0.0451
-124.0048 117.6860
0.8541 -0.0328
0.1911 -0.2873
0.2088 0.0301
-0.7105 0.0268
0.8697 -0.2572
0.0137 -0.2018
0.3127 -0.1927
-1.5021 -0.1181
-0.7649 0.3468
-0.6816 -0.0080
-0.2052 0.0338
34
The training values determined for feedforward network are as follow;
Table 3.4 Original & Estimation Arrival Angle Value for 1st & 17th Users
Training Training
Original Original
Output Output
Value Value
First User 17th User
angtest(1,1)= angtest(:,17)=
0.0215 0.0051
-124.0048 117.6860
-0.0166 0.0003
0.0025 -0.0088
0.0067 0.0084
-0.0035 -0.0066
0.0062 0.0086
-0.0190 -0.0015
0.0097 -0.0039
0.0252 -0.0041
0.0407 0.0049
-0.0277 -0.0090
0.0078 0.0026
35
As a second study, unlike the classification method, instead of classifying the
output, it produces a single output according to the target value defined according to
the angle value from the system trained according to the signal quality. Error was
calculated by comparing these outputs with the required angle. Results determined
for the angle values found in the ranges <-45,45> and <-90,90> and corresponding
measurements accordingly.
• The training values determined for Feedforward Neural Network are as follow;
It works slower than the feedforward neural network and Bayezian Regulation is
used as the train function. It is slower than the Levenberg-Marquardt
backpropagation train function, but provides improved output accuracy when
working with large challenging data. In Figure 3.12 and 3.13 show the results of
regression value and Figure 3.18 and 3.19 show the results of Error Graph for
elman neural network. Also better than feedforward neural network results.
• The training values determined for Fitting Neural Network are as follow;
36
3.3.1 Graph of Results
Figure 3.10 Error Graph Feedforward Neural Network for interval <-45,45>
Figure 3.11 Error Graph Feedforward Neural Network for interval <-90,90>
37
Figure 3.12 Error Graph Elman Neural Network for interval <-45,45>
Figure 3.13 Error Graph Elman Neural Network for interval <-90,90>
Figure 3.14 Error Graph Fitting Neural Network for interval <-45,45>
Figure 3.15 Error Graph Fitting Neural Network for interval <-90,90>
38
Figure 3.16 Regression Output Feedforward Neural Network for <-45,45>
39
Figure 3.18 Regression Output Elman Neural Network for <-45,45>
40
Figure 3.20 Regression Output Fitting Neural Network for <-45,45>
41
3.3.2 Challenges and Solutions
The reaction of the system to any random signal will be as follows: The system
is expected to produce 2 outputs for the user according to the incoming data. These
outputs are at the same distance from the base station but at different angle values. The
system measures the SINR on the user again with a 10 degree change, determines its
direction according to the improvement or worsening condition, and shapes the signal
according to the angle at the relevant limit value in the neural Network. In this way, the
problem is eliminated with an additional short-term measurement in the Beamforming
algorithm for different users at the same distance and with the same SINR value.
3.4 Comparison
According to all training algorithms, the results obtained in the range of <-90,90>
have a higher accuracy rate. The biggest reason for this is that the separation of users
is easier in a wider area. The results may be more accurate if it is studied only for users
with an angle of incidence greater than zero.
42
CHAPTER FOUR
CONCLUSION
In this paper, by using the neural network structure, the signal level and arrival
angle are calculated according to the location of the users, and it is aimed to provide
maximum quality service for a base station and to improve user satisfaction. The
feedforward, elman and fitting neural network algorithms were examined
comparatively.
The studies conducted in (Sallom & Ahmed, 2015) and (Güreken, 2009) are similar
to the approaches in our thesis, but they differ in method. In both studies, the error
calculation was made according to the desired and trained angle values obtained by
the neural network study for the location of the user. In our study, as a more complex
structure, the neural network algorithm was used in order to estimate the angle of
arrival according to the signal levels received from the users and also to estimate the
current location of the user.
In (Maja Sarevska, 2008), the blind beamforming study was analyzed and a weight
estimation was made by running the neural network for the user whose location is
unknown. Similarly, in our thesis, the arrival angle and signal level were determined
according to the location of the users at first, but the angle estimation was made
according to the signal level in the training part. In this respect, the two studies are
similar, and the radial basis neural network, which is an artificial neural network, was
used as the neural network algorithm, like the elman neural network we use.
In (Yugo M. Kuno & Madhu, 2019) by using neural network and beamforming
43
together, the traditional beamforming structure was compared and it was aimed to
send a more specific signal to the target user, that is to give service, by reducing the
side lobe and noises of the NN. The training data includes interfering and target signal
direction, ramdom amplitudes and phases and additive noise. In this way, it is aimed
to obtain a better quality signal by learning the noise shape and direction of arrival.
The minimum variable distortionless resporse bemformer (MVDR) and capon
beamformer are used to transmit signal to the target user in the maximum possible
way. This thesis is different from the techniques and purpose we use, but in further
studies, it is possible to provide a higher quality service by estimating the location of
use with neural network by combining this study and the techniques we use.
In (Mizumachi, 2019), showing similar aspects with the previous study, but aimed
to use this study together with beamforming and deep neural network structure in order
to reduce the noise on the speech signal and to obtain a quality speech signal. In this
study, a different training algorithm than ours is used, and by combining it with our
study in future studies, both the location of the user can be quickly determined and
a very high quality service can be provided by reducing the unwanted noise on the
speech signal by giving a quality signal.
In (Singh & Jayakumar, 2020), RMSE (Root Mean Square Error) was used as a
value indicating how much difference there is between target and calculated values.
The linear regression model was used as the neural network model. Linear regression
is a machine learning model and is a useful method for mapping inputs and outputs. In
our thesis, the neural network structure, which is one of the sub-branches of machine
learning, has been examined. Both studies differ in this respect and are similar in terms
of method and purpose. Both studies make angle estimation as a result of the training
algorithm.
As a further study of this thesis, beamforming will be made according to the user
density and the coverage will be directed to the region where the user is dense. With
machine learning, the hours of these user densities will be determined and
beamforming will be run before the user density.
44
REFERENCES
Ali, E. I., & Nordin, R. (2017). Beamforming techniques for massive mimo systems in
5g: overview, classification, and trends for future research. Frontiers Inf Technology
Electronic Eng, 18, 753–772.
Basu, D. (2010). Dictionary of Pure and Applied Physics 2nd ed. Florida: CRC Press.
45
Guanghua Ren, Yuting Cao, S. W. T. H., & Zeng, Z. (2018). A modified elman neural
network with a new learning rate scheme. Neurocomputing, 286, 11–18.
Güreken, M. (2009). Neural network based beamforming for linear and cylindrical
array applications. Middle East Technical University, 1–5.
Hebb, D. O. (1949). The Organization of Behavior. New York: The Orwell Press.
Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective
computational abilities. Proceedings of the National Academy of Sciences of the
United States of America, 79(8),2554–2558.
K. A. Gotsis, K. S., & Sahalos, J. N. (2019). On the direction of arrival (doa) estimation
for a switched-beam antenna system using neural networks. IEEE Transactions on
Antennas and Propagation, 57(5),1399–1411.
Le Magoarou, Luc, Y. T. P. S., & Crussière, M. (2021). Deep learning for location
based beamforming with nlos channels. Arxiv, 1–5.
Maja Sarevska, A.-B. M. S. (2008). Antenna array beamforming using neural network.
International Journal of Electronics and Communication Engineering, 2(12),2923
– 2927.
Mathworks (2020). White paper-hybrid beamforming for massive mimo phased array
systems.
46
Mizumachi, M. (2019). Neural network-based broadband beamformer with less
distortion. International Congress on Acoustics, 1–5.
Pai, A. (2020). Cnn vs. rnn vs. ann – analyzing 3 types of neural networks in deep
learning. https://www.analyticsvidhya.com.
P.Ioannides, & Balanis, C. (2005). Uniform circular arrays for smart antennas. IEEE
Antennas and Propagation Magazine, 47(4),192 – 206.
Sallom, A. H., & Ahmed, S. (2015). Elman recurrent neural network application in
adaptive beamforming of smart antenna system. International Journal of Computer
Applications, 129(11), 38–43.
Sean V. Hum (2006-2021). Ece422 - radio and microwave wireless systems. Class
Notes. https://www.waves.utoronto.ca/prof/svhum/ece422.html.
Sharma, P. (2009). Neural network based robust adaptive beamforming for smart
antenna system.
Singh, A. J., & Jayakumar, M. (2020). Machine learning based digital beamforming for
line-of-sight optimization in satcom on the move technology. 2020 4th International
Conference on Electronics, Communication and Aerospace Technology (ICECA),
422–427.
47
Tougaw, D. (2018). Applied Electromagnetic Field Theory. Valparaiso: Valparaiso
University.
Warren, M., & Pitts, W. (1943). A logical calculus of ideas immanent in nervous
activity. Bulletin of Mathematical Biophysics, 5, 115–133.
Xu Y., Liu X., C. X., & C., H. (Oct,2021). Artificial intelligence: A powerful paradigm
for scientific research. Innovation (Camb).
Yongxu Zhu, Jun Zhang;Jiangzhou Wang, A. P. P. W. X., & Zheng, G. (2019). Deep
learning based beamforming neural networks in downlink miso systems. 2019 IEEE
International Conference on Communications Workshops, 1–5.
Yugo M. Kuno, B. M., & Madhu, N. (2019). A neural network approach to broadband
beamforming. Proceedings of the 23rd International Congress on Acoustics,
6961–6968.
Zaremba Wojciech, S. I., & Oriol, V. (2014). Recurrent neural network regularization.
ArXiv, abs/1409.2329.
48